We have now seen how to work 1-D kinematics problems, and how to do vector arithmetic.  We are now going to put these two skills together and see how to work out 2-D kinematics problems. Despite the fact that we now have two dimensions to work with instead of just one, you’ll see that there is really not much more reasoning that goes into these problems — they’re really just like 1-D problems! We just break the problem up into two independent motions — usually called the motion in the x- and y-directions.

A special but very important case of 2-D motion is 2-D free-fall motion at the earth’s surface.  Recall that, in this case, the only force dictating the object’s motion is the earth’s gravitational force, in which case the acceleration is the acceleration due to gravity, g = 9.8 m/s² directly towards the earth’s center.  In this special case (and in this case only!), if the y-direction is taken to be vertical (we may call it positive upwards or downwards — it’s up to us!), then the motion in the x-direction is described by only one equation. This equation is simply the equation for average x-component of velocity (can  you remember back that far?), and is given, along with the kinematic equations of motion, in the next web page for your convenience.